Abstract
Let G be a polycyclic group and α a regular automorphism of order four of G. If the map φ: G → G defined by g φ = [g,α] is surjective, then the second derived group of G is contained in the centre of G. Abandoning the condition on surjectivity, we prove that C G (α 2) and G/[G, α 2] are both abelian-by-finite.
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We thank the referees for their time and comments.
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Supported by National Natural Science Foundation of China (Grant No. 11371124), Youth Foundation of Hebei Educational Committee (Grant Nos. QN2016184 and F2015402033) and Graduate Education Teaching Reform Foundation of Hebei University of Engineering (Grant No. 161290140004)
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Xu, T., Liu, H.G. Polycyclic groups admitting a regular automorphism of order four. Acta. Math. Sin.-English Ser. 33, 565–570 (2017). https://doi.org/10.1007/s10114-016-4660-y
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DOI: https://doi.org/10.1007/s10114-016-4660-y